论文标题
凯奇（Cauchy
Cauchy's work on integral geometry, centers of curvature, and other applications of infinitesimals
论文作者
论文摘要
就像他的ecole Polytechnique的Prony，Petit和Poisson的同事一样，Cauchy在他的研究和教学中都使用了Leibniz-Euler传统中的InfiniteSimals。凯奇（Cauchy）在1826年的差异几何形状中应用了无限量，其中无穷小数量既不是可变数量也不是序列，而是用作数字。他还在1832年的一篇关于积分几何形状的文章中应用了无限量，与数字类似。我们探讨了库奇（Cauchy）在教科书和研究文章中使用的这些和其他应用。 对凯奇（Cauchy）作品挑战的细心阅读对库奇（Cauchy）在分析和几何学史上的作用的看法。我们证明了凯奇（Cauchy）在几何概率，差异几何形状，弹性，狄拉克三角洲功能，连续性和收敛等多样性中的无限技术的生存能力。 关键词：凯奇 - 克罗夫顿公式；曲率中心；连续性；无穷小；积分几何；极限；标准零件； de prony;泊松
Like his colleagues de Prony, Petit, and Poisson at the Ecole Polytechnique, Cauchy used infinitesimals in the Leibniz-Euler tradition both in his research and teaching. Cauchy applied infinitesimals in an 1826 work in differential geometry where infinitesimals are used neither as variable quantities nor as sequences but rather as numbers. He also applied infinitesimals in an 1832 article on integral geometry, similarly as numbers. We explore these and other applications of Cauchy's infinitesimals as used in his textbooks and research articles. An attentive reading of Cauchy's work challenges received views on Cauchy's role in the history of analysis and geometry. We demonstrate the viability of Cauchy's infinitesimal techniques in fields as diverse as geometric probability, differential geometry, elasticity, Dirac delta functions, continuity and convergence. Keywords: Cauchy--Crofton formula; center of curvature; continuity; infinitesimals; integral geometry; limite; standard part; de Prony; Poisson
